How Far is the Boat From its Original Position?

[Benjamin_harsh]

Homework Statement

How far from its original position is the boat now?

Relevant Equations

With reference to ground, the water travels downstream for 2.5+3.5= 6 hours.
With reference to water, the boat went upstream for 1 hour. So the boat is

10/3×6−15/2×1=12.5 km downstream from the start.

A boat goes upstream for 3 hr 30 min and then goes downstream for 2 hr 30 min. If the speed of the current and the speed of the boat in still water are 10/3 kmph and 15/2 kmph respectively, how far from its original position is the boat now?

With reference to ground, the water travels downstream for 2.5+3.5= 6 hours.
With reference to water, the boat went upstream for 1 hour. So the boat is

Final Equation: 10/3×6−15/2×1=12.5 km downstream from the start.

Why should we solve this question through references?

How boat went upstream for 1 hour if question clearly says boat goes upstream for 3 hr 30 min?

 

[phinds]

How boat went upstream for 1 hour if question clearly says boat goes upstream for 3 hr 30 min?

You seem to have stated the problem twice with different values. What is the actual statement of the problem, as stated wherever you got it from?

 

[Benjamin_harsh]

You seem to have stated the problem twice with different values. What is the actual statement of the problem, as stated wherever you got it from?

Why should we solve this question through references?

 

[Mark44]

Why should we solve this question through references?

Because the boat is moving through the water, which is itself moving. If the boat's speed was only 10/3 km/hr, and it was traveling upstream, it would stay in the same place, relative to the ground, but would have traveled 10/3 km in an hour, relative to the water.

 

[SammyS]

Why should we solve this question through references?

What references are you referring to?
Frames of Reference?

Moving on, in an effort to see how you attempted to solve this problem:
The information in your original post appears to be rather scrambled. I did manage to pick out the actual problem.

A boat goes upstream for 3 hr 30 min and then goes downstream for 2 hr 30 min. If the speed of the current and the speed of the boat in still water are 10/3 kmph and 15/2 kmph respectively, how far from its original position is the boat now?​

Then fast forward to what you call the

Final Equation: 10/3×6−15/2×1=12.5 km downstream from the start.​

I agree that this is the correct answer numerically, but does this solution make sense?

Let's see. 10/3 (km/h) is the speed of the water. That's downstream and with respect to (w.r.t) dry land.
Also, 15/2 (km/h) is the speed of the boat in still water. I.e. The boat travels at a speed of 15/2 (km/h) w.r.t. the water.
Digging through the OP, we find your explanation of where the 6 and the 1 come from and that both are in units of hours.

With reference to ground, the water travels downstream for 2.5+3.5= 6 hours.​

With reference to water, the boat went upstream for 1 hour.​

(By the way: I notice that your solution does use references.)

Multiplying 10/3 km/h by 6 h makes sense and could possibly be useful in solving this problem.

But, what do you mean by "the boat went upstream for 1 hour"? You then multiply this by the speed of the boat w.r.t. the water, which you subtract from the distance the water moved in the entire 6 hours.
The boat goes upstream for 3.5, not just 1 hour, then goes downstream for another 2.5 hours.

You have the boat going upstream for just 1 hour, then what? What does it do the other 5 hours?

You haven't fully explained your reasoning here.
.

 

[Benjamin_harsh]

With reference to ground, the water travels downstream for 2.5+3.5= 6 hours.
With reference to water, the boat went upstream for 1 hour.

How boat went upstream for 1 hour only if question clearly says boat goes upstream for 3 hr 30 min?

My doubt regarding the way of approach to answer.

 

[phinds]

How boat went upstream for 1 hour only if question clearly says boat goes upstream for 3 hr 30 min?

My doubt regarding the way of approach to answer.

"A boat goes upstream for 3 hr 30 min and then goes downstream for 2 hr 30 min". 3.5hr - 2.5hr = 1hr

 

[SammyS]

How boat went upstream for 1 hour only if question clearly says boat goes upstream for 3 hr 30 min?

My doubt regarding the way of approach to answer.

So, that solution to the problem in the Original Post is not your solution? I misunderstood that.

Was that solution given to you written out in the manner you posted ? It does seem to me that the approach is somewhat unusual.

 

[Benjamin_harsh]

It does seem to me that the approach is somewhat unusual.

Can you show me another simple approach ?

 

[SammyS]

Can you show me another simple approach ?

Yes, we can get you started on another approach. But first ...

As to the question asked:

Why should we solve this question through references?

It is absolutely necessary due to the information given in the problem itself. The two given speeds are in reference to different objects: the land for the water, the water for the boat. Right?

Now for an alternate approach:
What is the boat's speed relative to land on the upstream portion of the trip?
What is the boat's speed relative to land on the downstream portion of the trip?